






import torch

from diffusers import DiffusionPipeline
class        a       (					lowercase__  ):



      """simple docstring"""


      def __init__( self   :     Optional[Any]						, __lowercase   :     Dict						, __lowercase   :     Union[str, Any]   )				-> Any:
        super().__init__()

        self.register_modules(unet=__lowercase						, scheduler=__lowercase   )




      def __call__( self   :     Union[str, Any]   )				-> str:
        __UpperCAmelCase				:      List[Any]	 =    torch.randn(
            (1, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)						, )
        __UpperCAmelCase				:      List[str]	 =    1

        __UpperCAmelCase				:      List[str]	 =    self.unet(__lowercase						, __lowercase   ).sample
        __UpperCAmelCase				:      str	 =    self.scheduler.step(__lowercase						, __lowercase						, __lowercase   ).prev_sample

        __UpperCAmelCase				:      Optional[Any]	 =    scheduler_output - scheduler_output + torch.ones_like(__lowercase   )

        return result




from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def a__       (			A_   ):






  '''simple docstring'''





  __magic_name__								=			prime_factors(A_   )
  if is_square_free(A_   ):
    return -1 if len(A_   ) % 2 else 1
  return 0


if __name__ == "__main__":
    import doctest

    doctest.testmod()

